Transcript A1 8.2 - MillerMath

8.2 Dividing Monomials
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Algebra 1
Glencoe Mathematics
8-2 Dividing Monomials
pages 417-423
What You’ll Learn
•Simplify expressions involving the
quotient of monomials
•Simplify expressions containing
negative exponents
How How can you
compare pH levels?
table on page 417
c = concentration of hydrogen ions
æ1 öpH
c = ççç ÷
÷
çè10 ÷
÷
ø
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Vocabulary
Quotients of
Monomials
zero exponent ; negative
exponent
Key Concept
Words
Quotient of Powers
Symbols
Why can’t a
be zero?
To divide two powers that
have the same base, subtract
the exponents.
For all integers m and n
and any nonzero number a,
am
an
Example
b15
b7
= am-
n
= b15-
7
or b8
Stop: Let’s look at Example 1
Simplify
5 8
a b
3
ab
=
a5b8
ab3
a5b8
a1b3
= a5- 1b8-
3
= a 4b5
a
m
n
a
= a
m- n
Stop: Let’s learn the Miller
method
Simplify
a5b8
ab3
=
a5b8
ab3
a 4b5
aaaaabbbbbbbb
(
)
abbb
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Key Concept
Words
Power of a Quotient
To find the power of a quotient,
find the power of the numerator
and the power of the
denominator.
Symbols
For any integer m and
any real numbers a and
m
æ
ö
b, b≠0 ç a ÷
am
=
çç ÷
÷
çèb ÷
ø
bm
Example
æc ö5 c5
çç ÷
=
ççè d ÷
÷
÷
ø
d5
Stop: Let’s look at Example 2:
4
æ2p2 ö
÷
 Simplify ç
çç
÷
ççè 3 ÷
÷
÷
ø
4
æ2p2 ö
çç
÷
÷
çç
÷
çè 3 ÷
÷
ø
4 2×4
=
2 p
4
3
8
16p
=
81
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Negative Exponents
Study Tip p418
How do you change a
decimal to a fraction
with the graphing
calculator?
Study Tip p419
See Miller Method for
example 1
To change a number to a fraction
press MATH ENTER ENTER
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Key Concept
Zero Exponent
Words
Symbols
Example
Any nonzero number
raised to the zero power
is 1.
a0 = 1
(-0.25)0 = 1
STOP. Let’s look at Example 3:
Simplify
0
5 ö
A) æ
ç 3x y ÷
çç
÷
=1
÷
ççè8xy7 ÷
÷
ø
B)
3
t
(1)
t s
=
=
t
t
3 0
t3
=
t
t2
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Key Concept
Negative Exponent
Words
For any nonzero number a
and any integer n,
a-n is the reciprocal of an.
In addition, the reciprocal
of a-n is an.
Symbols For any nonzero number a
and any integer n,
- n
a
Example
5-
2
=
=
1
an
1
2
5
and
or
1
25
1
a- n
1
m-
3
= an
= m3
Stop. Lets look at Example 4:
(the Miller method)
Simplify
- 3 2
A)
b
c
- 5
d
2 5 Negative exponents
=
c d
3
b
- 4 7
- 3a
B)
b
2 7 - 5
21a b c
change to other
side of fraction bar
-1
7 5
=
=
- 3b c
2 4 7
21a a b
5
- c
7a
6
=
7 5
- 3b c
6 7
21a b
7
SKIP Example 5
Homework p421
15-37odd